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Mathematical Charts and Tables

Special Purpose Tables

Special Purpose Tables

From at least the 1930s through the 1960s, American manufacturers distributed a variety of tables that customers might use. This was sometimes in the form of a pamphlet, such as the set of miscellaneous hydraulic tables for designers prepared by the Southwark Foundry and Machine Company Division of Baldwin-Southwark Corporation in 1931. Other special purpose tables, distributed on slide charts of various sorts, described properties of such materials as leaded bronze, nickel alloys, specialty steels, wire cloth, glass, and salt/water mixtures. Others gave properties of compressors, elements of screw threads, and data on the dietary advantages of various forms of meat, The Aetna insurance company prepared a table instructing drivers on the safe distances to be maintained between cars. As late as 1969, a manufacturer of paper goods distributed a slide chart for calculating the cost per ounce of groceries, and urged consumers to make careful comparisons of prices. Some tables were not associated with any specific product. Thus the “Menu Minder,” distributed in the mid-1970s, allowed one to quickly alter recipes to serve more or fewer people. It may have been distributed as a kitchen novelty by any number of firms.

Tables distributed by business machine manufacturers have been mentioned already. In addition to covering the needs of commerce and special forms of manufacturing, some of these offered ways to estimate square roots and cube roots.

Specialized tables also were prepared for government use. Military contractors prepared tables to assist in aiming guns and filling out Air Force inventory forms. The Atomic Energy Commission prepared a table for use in uranium enrichment plants.

Manufacturers compiled and distributed tables for designers who would use their products. This 32-page pamphlet, published in August, 1931, by the Southwark Foundry and Machine Company Division of the Baldwin-Southwark Corporation, brought together data “of particular interest and value” to those “engaged in the use of hydraulic equipment - particularly those structures involving the use of hydraulic pressures for load-producing purposes.”

Tables included give:

1. the circumferences and areas of circles of diameters ranging from 1/64” to 98.”

This paper slide chart has a blue-gray envelope that includes a sliding chart printed in black on white. It served as an advertisement for the leaded bronzes produced by Sumet Corporation of Buffalo, New York.

A window on the front of the envelope reveals a column of the slide that lists the commercial designation of a Sumet product, and its chemical composition (mainly copper and lead, with varying amounts of tin, and some zinc, nickel and phosphorus). Also listed for the product are such physical properties as tensile strength, elongation, Brinnell hardness, static load, and weight (in pounds per cubic inch). A window on the back shows a listing on the slide of the general applications of the same bronze.

A mark on the front reads: Technical Data (/) for LEADED BRONZE. A mark on the back reads: SUMET CORP., BUFFALO, N. Y. A copyright sign precedes the company name.

Bronzes with commercial designation from SM-4 through SM-18 were being produced by Sumet Corporation from at least 1931 to at least 1937. Hence the rough date of 1935 assigned to the object.

This small slide chart allows motorists to find their “danger zone,” that is to say the distance an automobile will move forward in feet after a motorist wishes to stop, as this varies with the speed of the car (ranging from 20 to 80 miles per hour) and the reaction time of the driver (ranging from 1/4 second to 1 second). The total stopping distange or “danger zone” ranges from 29 feet to 469 feet.

The envelope and slide are of white paper, printed in red and black. A mark on the front, the back and one side of the slide reads: COPYRIGHT, 1935, AETNA CASUALTY & SURETY CO.

Companies seeking to provide customers with advertisements they might consult repeatedly sometimes distributed convenient mathematical tables. This is an example of one of these. The small white plastic card has figures printed in black. The table gives approximate conversions between the figures obtained from several different methods of measuring the hardness of nickel alloy steels. The numbers are associated with the Brinnell, Vickers or Forth, Rockwell, and Shore scales, as well as the tensile strength.

One edge of the table contains a scale 10 centimeters long, divided to millimeters. The other contains a scale 4 inches long, divided to 1/20th of an inch.

The reverse of the table describes the advantages of Ryerson certified steels. It is marked in part: 75C 2-39. It is also marked: PRINTED (/) IN (/) U.S.A.

This slide chart, distributed by the Qunicy Compressor company of Quincy, Illinois, is designed to allow customers to select the appropriate model of Quincy air compressor to purchase, knowing the pressure at which the air is to be delivered and the number of cubic feet per minute of air delivery desired. On one side, pressures range from 30 to 100 pounds On the other, they range from 110 to 250 pounds. For each model, the chart indicates the horsepower, speed, and piston displacement.

The chart consists of a paper envelope held together with metal rivets and a paper slide that moves crosswise. A mark near the bottom reads: Copyright 1941 Perry Graf Corp. Maywood, Ill. Slide charts made by Perry Graf that are in the Museum collections include 1979.3074.03, 1983.3009.04, 1983.3009.05,1983.3009.06, 1987.0108.03, and 1988.0325.01, and 1988.3076.01.

This paper model slide chart has an envelope held together by staples and a rectangular slide, It contains tables relating to the size and shape of screw threads, as standardized in the mid-20th century United States. Tables on one side are for the “National Fine Series,” those on the other side for the “National Coarse Series.” Fine screws move a relatively short distance each time the screw is turned, and have greater locking power.

Assuming that screws are of the general form proposed by William Sellers of Philadelphia in 1864, the chart gives the depth of the thread element, the width of the flat portion of the base, the tap drill size to be used in fabricating the screw, and the best wire size for measuring the screw (that is to say, the wire size that will just touch the thread at the pitch diameter). It also indicates the maximum and minimum dimensional tolerances for different classes of fit from the loosest (class 1) to the most precise (class 4).

A mark on the front reads: QUICK SLIDE (/) THREAD ELEMENTS. A mark on the back reads: COPYRIGHT 1946 BY CAPELL DESIGNING CO. BOX 993 CHURCH ST. STA. NEW YORK 8, N.Y. The back is stamped: [copyright symbol]CI I pub. 430. Below this is the date stamp: FEB - 7 1946. A nearby stamp reads: SURPLUS (/) DUPLICATE and shows the seal of the Library of Congress.

Rockford D. Robbins and John E. Capell of New York copyrighted the instrument in February of 1946. It seems likely that this was the copy of their device submitted to the Copyright Office of the Library of Congress. No manufactured example of the instrument is yet known.

References:

Bruce Sinclair, “At the Turn of a Screw: William Sellers, the Franklin Institute, and a Standard American Thread,”

Technology and Culture , vol. 10, No. 1 (Jan., 1969), pp. 20-34

United States Library of Congress, Catalog of Copyright Entries 1946 Works of Art . . .

This slide chart advertises the properties of the ELASTUF machinery steels manufactured by Beals, McCarthy & Rogers, Incorporated, of Buffalo, New York. It consists of a paper envelope with metal rivets and a paper slide. Lining up an arrow on the slide with a type of steel listed along the top of the front reveals in a window of the envelope a general description of the properties of the steel. The other side of a chart shows the physical properties of that type of steel (its tensile strength, yield point, elongation and reduction) for different bar sizes.

A mark along the bottom right of the back reads: COPYRIGHT 1947 BEALS, McCARTHY & ROGERS, INC. A mark on the slide reads: MANUFACTURED BY (/) GRAPHIC CALCULATOR CO. (/) CHICAGO 5, ILL. (/) MADE IN U.S.A.

For other products of Graphic Calculator Company, see 2000.3029.02 and 2000.3029.13.

Graphic Calculator Company was a slide rule and slide chart manufacturing and design company founded in Chicago in 1940 by Capron R. Gulbransen, and apparently still in business at the time of Gulbransen’s death in 1969. By 1965, the firm had moved to Barrington, Illinois.

Mathematical tables like this one were distributed by producers to persuade consumers of the value of their products. This instrument consists of a disc with a smaller disc that rotates above it. A metal clasp at the center holds the two pieces together. A slot in the upper disc reveals one column of the table printed on the disc below. This table gives the percentage of daily recommended dietary allowances supplied by a 3.5 oz serving of beef, lamb, pork, and veal. The percentages are given for children of ages 3-4 years, 4-6 years, 7-9 years, and 10-12 years; teenaged boys 13-15 and 16-19 years old; teenaged girls 13-15 and 16-19 years old; women of ages 25, 45, and 65; and men of ages 25, 45, and 65. The daily requirements of protein, calories, iron, thiamine, riboflavin, and niacin supplied by a serving of meat are indicated. The back lists the nutrition provided by strained meat fed to infants and gives references for the calculations. These references date from 1950 and 1958.

The instrument is marked on the front: The percentages of (/) daily recommended dietary (/) allowances supplied by one (/) 3 1/2 oz. serving of cooked MEAT for moderately active children and adults. It is marked on the front and the back: NATIONAL LIVE STOCK AND MEAT BOARD. It is marked on the back: A Product of Graphic Calculator Co., Chicago 5, Ill.

Graphic Calculator Company was a slide rule and slide chart manufacturing and design company founded in Chicago in 1940 by Capron R. Gulbransen, and apparently still in business at the time of Gulbransen’s death in 1969. By 1965, the firm had moved to Barrington, Illinois.

By the mid-20th century, industrial chemists had introduced a form of hydrometer for measuring brine strength from the density of a water/salt solution at a known temperature. This rotating table allows one to find the chemical properties of solutions of sodium chloride (common table salt) in water at a temperature of 60 degrees Fahrenheit in degrees of the “salometer scale.” By definition, the salometer degree indicates percentage of saturation of a salt solution. For example, a reading of 70 indicates 70% saturation. Hence the scale runs from 0 to 100.

The slide chart consists of two paper discs of the same size, with a third slightly larger disc between them. The middle disc is elongated at one end and has a hole so that it may be suspended. A metal rivet holds the discs together at the center. Cutouts in the two smaller discs allow one to read tables printed on the central disc. The front of the instrument has tables for 0 to 50, and the reverse for 51 to 100. For each salometer degree, the table lists such chemical properties of the solution as its specific gravity, the percentage by weight of sodium chloride, the weight in pounds of one gallon of brine, the number of pounds per gallon of brine of both sodium chloride and water, the weight of one cubic foot of brine, the number of pounds per cubic foot of both sodium chloride and water, the number of gallons of water per gallon of brine, the number of pounds of salt per gallon of water, and the freezing point in degrees Fahrenheit. Another table indicates how one should adjust readings in degrees salometer when measurements are taken at temperatures other than 60 degrees Fahrenheit.

A mark on the top disc reads: BRINEMASTER (/) dial-a-brine. A second mark there reads: Diamond Crystal Salt Company (/) ST. CLAIR, MICHIGAN. A mark on the bottom disc reads: Slide-Chart Copr. [sic] 1962, PERRYGRAF Corp., Maywood, Ill.

The salinity of brines was expressed in salometer degrees from at least the 19th century.

References:

L. C. Beck, “Report on the Mineralogical and Chemical Department of the Survey,” In Assembly: State of New York, Issue 150, 1841, p. 18.

E. Meriam, “American and Foreign Salt,” Sixth Annual Report of the American Institute of the City of New York, 1848, p. 207.

This slide chart has a plastic sleeve that holds a cardboard slide. One side of the slide has a table giving the properties of various forms of filter cloth and wire cloth. The other side has two graphs.

The Multi-Metal Wire Cloth Company distributed this plastic slide chart to allow its customers and potential customers to compare the flow rates and particle retention of various forms of woven wire and woven fabric. Results were based on observations carried out at Columbia University. A paper sticker attached to the back of the sleeve gives further details of the calculation.

A mark on the front of the sleeve reads: MM (/) CALCULATOR. A mark on the back of the sleeve reads: Multi-Metal (/) WIRE CLOTH COMPANY, INC. (/) 1350 GARRISON AVE. (/) NEW YORK 59, NEW YORK (/) PRINTED IN USA COPYRIGHT 1959. The slide and the paper envelope are stamped: SEP 18 1963.

This object came to the Smithsonian as part of a large collection of trade literature relating to meat processing donated by the Cincinnati Boss Company of Cincinnati, Ohio.